which is called the discrete nonlinear Schrödinger equation[1]}, [2]}. There are two conserved quantities. One is the Hamiltonian[3]}, [4]}, [5]},
\(H=\sum _{n=1}^{N}\left( \varepsilon \left|\psi _{n+1}-\psi _{n}\right|^{2}-\frac{\xi }{2}\left|\psi _{n}\right|^{4}\right) .\) 
